U.S. Pat. No. 5,321,991 describes a clamp-on Coriolis mass flow meter. Patent WO 03/021205 describes a calibration method for Coriolis mass flow meters. A Coriolis mass flow meter makes use of the transverse forces that are generated in a flowing liquid if the pipe is subject to vibrations transverse to the direction of flow. When the liquid flows through a pipe that is vibrated transversely to the axial direction of the pipe, then an imaginary slice of the liquid in a transverse cross section of the pipe exerts a Coriolis transverse force on the pipe which is strictly linearly proportional to the total mass flow of that segment. By measuring the resultant effect on the deflection of the pipe, a measurement is obtained that is a measure for the mass flow.
The prior art makes use of a vibration model in terms of vibration modes. The vibration model assumes that a clamped pipe has a number of vibration modes (labeled with an index “m”), in each of which the pipe, if the mass flow was zero in the absence of excitation, could vibrate, damped, with a deflection transverse to the pipe ofum(x,t)=C(t)sm(x)The x dependency sm(x) of this vibration for a particular mode m is called the mode shape. What is specific about this model is that in a vibration mode there is a time-independent proportion factor between the deflection at different positions x.
The mode shape is generally dependent on the properties of pipe 10 and its clamping.
The vibration frequencies of the different modes determine the resonance frequencies of the pipe. When the pipe is deflected with a time periodic signal exp(iωt) of a frequency at or near the resonance frequency of a particular mode, the deflections u(x,t) of the pipe are mainly determined by the mode shape sm(x) of the respective mode:u(x,t)=Bmsm(x)exp(iωt)In the absence of a mass flow and at minor damping, the deflections u(x,t) in this single mode at all positions x are in phase. In the presence of a mass flow Q, a place-dependent transverse force Fc on the pipe arisesFc=2Q d2u/dxdt This force causes a coupling between the modes, as a result of which deviations arise between the deflection u(x,t) and the shape of the resonant mode shape, having the shape of the mode shapes of other modes.
In the prior art, the mass flow Q is measured by vibrating the pipe at the frequency of a particular mode and subsequently measuring the amplitude of the deflections of the pipe at points where in the absence of mass flow nodes in the vibration of the respective mode would occur. The measured vibration amplitude is thus a measure for the mass flow Q.
The deviations of the resonant mode are approximately ninety degrees out of phase with the resonant mode itself. This is sometimes also made use of in measuring the mass flow Q, for instance by measuring the phase differences of the zero-axis crossings at two different positions on the pipe, which are the result of the excitation of the resonant mode and non-resonant modes.
Both kinds of measurements are relative, in the sense that changes in the mass flow Q can be measured with them, but one or more calibration factors are needed to be able to measure the mass flow in an absolute sense. The calibration factors depend on the specific properties of the pipe, which are often dependent on external influences such as the temperature. In the case of “inline” Coriolis mass flow meters, which are fabricated pipe-and-all and are later installed in a pipe system, the calibration factors can already be determined before mounting. In clamp-on Coriolis flow meters which are mounted externally on pipes of an existing pipe system, the calibration factors can only be determined after mounting.
Normally, the calibration factors are determined empirically, by measuring the response at at least two different given mass flows of known flow strength. By virtue of the strict linearity, the meter is thus fully calibrated. WO03/021205 describes how a calibration factor can be calculated on the basis of modal mass, damping and stiffness parameters and mode shapes such as these can be determined with the aid of standard modal analysis techniques. Thus, the mass flow meter can also be calibrated if it is not possible to provide two different mass flows of known flow strength. It suffices in the absence of mass flow to measure information about the mode shapes, and subsequently to calculate what the response of the mass flow meter will be at other flow strengths.
If the modal properties of the pipe were determined at a mass flow that is not zero, it appears that this can significantly influence the calculated calibration factors. In a simulation example where the calibration factor would have to be 10.95 degrees per kg/sec for the phase offset and 0.168 degrees per kg/sec for the phase sensitivity, it appears that calculated calibration factors of, respectively, 10.11 degrees and 0.158 degrees per kg/sec are found if these are calculated with the modal parameters and mode shapes that follow from a standard modal analysis at a flow strength of 10 m/sec (corresponding to a mass flow of 88 kg/sec). The magnitude of the error depends on the specific configuration of the mass flow meter, and increases with increasing magnitude of the mass flow at which the modal analysis takes place. Therefore, for a result that is reliable under all circumstances in the use of the method according to the art of WO03/021205, measurement of the modal properties of the pipe in the absence of mass flow is necessary.
The normal operation of existing pipe systems must therefore be interrupted to be able to use the Coriolis mass flow meter whilst calibrated. Further, such a calibration is sensitive to changes of the properties of the pipe used, for instance through temperature variations or wear, which may necessitate repeated interruptions of the normal operation for recalibration.